Systems of Equations (Substitution)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does substitution mean in the context of solving equations?

Back

Substitution is a method of solving a system of equations by solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

How do you solve the system of equations: x = 6 and y = 2x - 3?

Back

Substituting x = 6 into y = 2(6) - 3 gives y = 12 - 3 = 9. The solution is (6, 9).

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does it mean if a system of equations has one solution?

Back

It means that the graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has no solution?

Back

It means that the graphs of the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinite solutions?

Back

It means that the equations represent the same line, and every point on the line is a solution.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of the equations plotted on a coordinate plane.

Tags

CCSS.8.EE.C.8A

Front

How do you determine the solution of a system of equations graphically?

Back

The solution is found at the point where the lines of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

Solve the system of equations: y = 8 and y = -4x + 4.

Back

Substituting y = 8 into -4x + 4 gives 8 = -4x + 4. Solving for x gives x = -1. The solution is (-1, 8).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve the system of equations: y = 3 - x and 3y + x = 5.

Back

Substituting y = 3 - x into 3y + x = 5 gives 3(3 - x) + x = 5. Solving gives x = 2 and y = 1. The solution is (2, 1).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6